时间：2022年11月6日

卜凯峰

Title: Quantum circuit complexity via optimal transport

Abstract: Quantum circuit complexity—a measure of the minimum number of gates needed to implement a given unitary transformation—is a fundamental concept in quantum computation, with widespread applications ranging from determining the running time of quantum algorithms to understanding the physics of black holes. In this talk, I will introduce our recent results on quantum circuit complexity via quantum optimal transport.

个人简介：Kaifeng Bu（卜凯峰）is a post-doctoral fellow mentored by Jaffe Arthur. He mainly focus on the optimal transportation and its applications to quantum information theory.

李建阁

Title:Forward and reverse entropy power inequalities

Abstract: Shannon's entropy power inequality, which plays a fundamental role in information theory and probability, may be seen as an analog of the Brunn-Minkowski inequality in convex geometry. In this talk, we survey various recent developments on forward and reverse entropy power inequalities and discuss close connections with classical inequalities in convex geometry and functional analysis.

个人简介：Jiange Li（李建阁）is with the Institute for Advanced Study in Mathematics at the Harbin Institute of Technology（哈尔滨工业大学）. Dr. Li's research interests lie at the interface between probability and analysis, including information-theoretic inequalities, the concentration of measure phenomenon, geometric functional inequalities, and the analysis of Boolean functions.

黄林哲

Title:Complete positivity of comultiplication and primary criteria for unitary categorification

Abstract: In this talk, I will introduce our recent work on applying quantum Fourier analysis to unitary categorifcation of fusion rings. We provide a family of analytic criteria for fusion rings’ unitary categorifcation, which are stronger than the Schur product criterion. Various examples of fusion rings will be given. These criteria could also be applied as obstructions of principal graphs of subfactors. It is a joint work with Zhengwei Liu, Sebastien Palcoux and Jinsong Wu.

个人简介：黄林哲是清华大学丘成桐数学科学中心博后，研究方向为泛函分析和量子傅里叶分析。

张明祖

Title: A novel view: edge isoperimetric methods and reliability evaluation of several kinds of conditional edge-connectivity of interconnection networks

Abstract: Reliability evaluation and fault tolerance of an interconnection network of some parallel and distributed systems are discussed separately under various link-faulty hypotheses in terms of different $\mathcal{P}$-conditional edge-connectivity. With the help of edge isoperimetric problem's method in combinatorics, this paper mainly offers a novel and unified view to investigate the $\mathcal{P}$-conditional edge-connectivities of hamming graph $K_{L}^{n}$ with satisfying the property that each minimum $\mathcal{P}$-conditional edge-cut separates the $K_{L}^{n}$ just into two components, such as $L^{t}$-extra edge-connectivity, $t$-embedded edge-connectivity, cyclic edge-connectivity, $(L-1)t$-super edge-connectivity, $(L-1)t$-average edge-connectivity and $L^{t}$-th isoperimetric edge-connectivity. They share the same values in form of $(L-1)(n-t)L^{t}$ (except for cyclic edge-connectivity), which equals to the minimum number of links-faulty resulting in an $L$-ary-$n$-dimensional sub-layer from $K_{L}^{n}$. Besides, we also obtain the exact values of $h$-extra edge-connectivity and $h$-th isoperimetric edge-connectivity of hamming graph $K_{L}^{n}$ for each $h\leq L^{\lfloor {\frac{n}{2}} \rfloor}$. For the case $L=2$, $K_2^n=Q_n$ is $n$-dimensional hypercube. Our results can be applied to more generalized class of networks, called $n$-dimensional bijective connection networks, which contains hypercubes, twisted cubes, crossed cubes, M\"obius cubes, locally twisted cubes and so on. Our results improve several previous results on this topic.

个人简介：张明祖，现为新疆大学副教授，硕士生导师，美国《数学评论》评论员。博士阶段师从厦门大学张莲珠教授，期间在美国西弗吉尼亚大学数学系学习一年,师从赖虹建教授。主要研究方向为图论及网络优化。在IEEE Transaction on Reliability、Discrete Applied Mathematics、Information Sciences、Theororetical Computer Science、Journal of Parallel and Distributed Computing等期刊发表SCI论文20余篇。目前主持在研项目4项，其中国家自然科学基金青年项目1项，省部级1项。